Discovering the structure of mathematical problem solving

Anderson, John R.; Lee, Hee Seung; Fincham, Jon M.

doi:10.1016/j.neuroimage.2014.04.031

Cited by 40Cognitive and developmental aspects of mathematical skillsMathematics Education and PedagogyNeurobiology of Language and Bilingualism

Discovering the structure of mathematical problem solving

Anderson, John R., Lee, Hee Seung, Fincham, Jon M.·2014·NeuroImage

DOI 10.1016/j.neuroimage.2014.04.031

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Abstract

The goal of this research is to discover the stages of mathematical problem solving, the factors that influence the duration of these stages, and how these stages are related to the learning of a new mathematical competence. Using a combination of multivariate pattern analysis (MVPA) and hidden Markov models (HMM), we found that participants went through 5 major phases in solving a class of problems: A Define Phase where they identified the problem to be solved, an Encode Phase where they encoded the needed information, a Compute Phase where they performed the necessary arithmetic calculations, a Transform Phase where they performed any mathematical transformations, and a Respond Phase where they entered an answer. The Define Phase is characterized by activity in visual attention and default network regions, the Encode Phase by activity in visual regions, the Compute Phase by activity in regions active in mathematical tasks, the Transform Phase by activity in mathematical and response regions, and the Respond phase by activity in motor regions. The duration of the Compute and Transform Phases were the only ones that varied with condition. Two features distinguished the mastery trials on which participants came to understand a new problem type. First, the duration of late phases of the problem solution increased. Second, there was increased activation in the rostrolateral prefrontal cortex (RLPFC) and angular gyrus (AG), regions associated with metacognition. This indicates th…

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Cognitive and Metacognitive Aspects of Mathematical Problem Solving: An Emerging Model
Yimer, A., & Ellerton, N. F. (2015)

Authors: Anderson, J. R., Lee, H. S., & Fincham, J. M.
Affiliations: Carnegie Mellon University (US)
Yonsei University (KR)
Corresponding author: Anderson, John R.
ORCID: Anderson, John R.
Lee, Hee Seung
Fincham, Jon M.
Venue: NeuroImage
Publisher: Elsevier BV
Published: 2014-08
Volume: 97
Pages: 163-177
ISSN: 1053-8119 (ISSN-L)
DOI: 10.1016/j.neuroimage.2014.04.031
OpenAlex: W2072055621
Cited by: 40
References: 56
Citations by year: 2026: 2 · 2025: 1 · 2024: 5 · 2023: 2 · 2022: 1 · 2021: 4 · 2020: 5 · 2019: 3 · 2018: 4 · 2017: 4 · 2016: 2 · 2015: 6 · 2014: 1
FWCI: 4.58
Type: journal article
Language: en
Open access: closed
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations: NeuroImage (publishedVersion)
PubMed (publishedVersion)
Funders: Institute of Education Sciences, U.S. Department of Education (R305A100109)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Cognitive and developmental aspects of mathematical skills
Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
Life Sciences › Neuroscience › Cognitive Neuroscience › Neurobiology of Language and Bilingualism
Keywords: mathematical problem solving, problem-solving phases, cognitive development stages, visual attention, default mode network, rostrolateral prefrontal cortex, angular gyrus, metacognition, reflection, hidden Markov models, multivariate pattern analysis
MeSH terms: Gestures, Humans, Image Processing, Computer-Assisted, Mathematics, Problem Solving, Transfer, Psychology, Echo-Planar Imaging

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Discovering the structure of mathematical problem solving

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